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Convert the following:

[tex]437_{10} = (?)_8[/tex]

Sagot :

GinnyAnsweridn
Sure, let's convert the decimal number [tex]\(437_{10}\)[/tex] to its equivalent in base 8 (octal).

### Step-by-Step Conversion:

1. Understanding the Process:
- Converting a decimal number to an octal number involves dividing the decimal number by 8 repeatedly and keeping track of the remainders.

2. Start with the Decimal Number:
- The given decimal number is 437.

3. Repeat the Division:
- Divide the number by 8 and record the quotient and remainder.

- First division: [tex]\(437 \div 8 = 54\)[/tex] with a remainder of [tex]\(5\)[/tex].
- Quotient: 54
- Remainder: 5

- Second division: [tex]\(54 \div 8 = 6\)[/tex] with a remainder of [tex]\(6\)[/tex].
- Quotient: 6
- Remainder: 6

- Third division: [tex]\(6 \div 8 = 0\)[/tex] with a remainder of [tex]\(6\)[/tex].
- Quotient: 0
- Remainder: 6

4. Read the Remainders from Bottom to Top:
- The remainders, read from bottom to top, give us the octal number: [tex]\(665\)[/tex].

### Conclusion:
So, the conversion of [tex]\(437_{10}\)[/tex] to base 8 (octal) is:
[tex]\[ 437_{10} = 665_8 \][/tex]
This means that the decimal number 437 is equal to 665 in octal.
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